Economic order quantity for joint complementary and substitutable items

In real-world situations, substitution may occur in the event of a product stock-out, and some products are complements with others. However, the classical inventory models ignore these conditions. This paper addresses an economic order quantity (EOQ) model to determine the joint ordering policy for two products under completion and substitution conditions. The proposed model determines order quantities for two products in order to optimize the total cost of inventory, including setup and holding costs. To formulate the problem, two special cases are discussed and analyzed in detail. Furthermore, the pseudo-convexity of the total cost functions is derived, and then a solution procedure is suggested. Numerical examples are presented and an analysis of sensitivity is conducted, using Matlab and Lingo solver, in order to investigate the impact of input parameters on the optimal policy. The results show that proposed model saves the costs as opposed to the traditional EOQ model.